 | Yale University - 1898 - 212 pages
...escribed, and circumscribed circles of any triangle. 3. (a) Two polygons are similar when composed of the same number of triangles, similar each to each and similarly placed, (b) When the areas of two similar polygons are in the ratio of in to n, in what ratio are the homologous... | |
 | Mathematics - 1898 - 228 pages
...greater. 3. Define similar polygons, similar sectors, similar segments. If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. 4. The areas of similar segments have the same ratio as the squares of the... | |
 | Webster Wells - Geometry - 1898 - 264 pages
...of a similar triangle is PROP. XX. THEOREM. 2566. Two polygons are similar when they are composed of the same number of triangles, similar each to each, and similarly placed. Given, in polygons AC and A'C', A ABE similar to A A'B'E', A BCE to &B'C'E', and A CDE to A C'D'E'.... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...and A'C' have their homologous sides proportional. PROP. XXI. THEOREM. 267. (Converse of Prop. XX.) Two similar polygons may be decomposed into the same...triangles, similar each to each, and similarly placed. A. Given E and E' homologous vertices of similar polygons AC and A'C', and lines EB, EC, E'B', and... | |
 | Webster Wells - Geometry - 1899 - 450 pages
...and A'C' have their homologous sides proportional. PROP. XXI. THEOREM. 267. (Converse of Prop. XX.) Two similar polygons may be decomposed into the same number of triangles, similar each to each, and simffv ly placed. Given E and E' homologous vertices of similar polygons AC and A'C', and lines EB,... | |
 | Harvard University - Geometry - 1899 - 39 pages
...proportional to the sides of the angle. THEOREM VI. 10 Conversely, if two polygons are similar, they can be decomposed into the same number of triangles, similar each to each and similarly placed. THEOREM VII. The perimeters of two similar polygons are in the same ratio as any two corresponding... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry, Modern - 1899 - 272 pages
...C 2 = = r. .-. AiBi + B1C1 + :A 2 B 2 + B 2 C 2 + =r. (Why?) 4. Two similar polygons can be divided into the same number of triangles similar each to each, and similarly placed. For 0 and O" coincide, and the figures can be placed having 0 within each. The triangles AiOBi, A^OB... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 400 pages
...C 2 = = r. .'. A^ + JBiCi + :A 2 B 2 + B 2 C 2 + = r. (Why?) 4. Two similar polygons can be divided into the same number of triangles similar each to each, and similarly placed. For 0 and Of coincide, and the figures can be placed having 0 within each. The triangles AiOB i , A... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...Theorem. 175. If two polygons are similar, the diagonals drawn from homologous vertices divide them into the same number of triangles, similar each to each, and similarly placed. B Hypothesis. ABCDEF and GHKMNO are similar polygons, and from the homologous vertices are drawn the... | |
 | Education - 1901 - 814 pages
...equal angles with the line ; the point to the center. 3 Prove that if two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar. 4 Complete and demonstrate the following : the area of a trapezoid is equal... | |
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If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. 
